Using Euclid’s division algorithm to find the HCF of 1488 and 37888:

To find the highest common factor (HCF) of two numbers using Euclid’s division algorithm, we need to perform a series of divisions until we reach a remainder of zero. Here is a step-by-step explanation of how to find the HCF of 1488 and 37888:

Step 1: Divide the larger number by the smaller number.
In this case, 37888 ÷ 1488 = 25.

Step 2: Find the remainder.
The remainder of this division is 188.

Step 3: Replace the larger number with the smaller number and the smaller number with the remainder.
Now, we have 1488 ÷ 188.

Step 4: Perform the division again.
1488 ÷ 188 = 7.

Step 5: Find the remainder.
The remainder of this division is 0.

Step 6: Stop the process.
Since we have obtained a remainder of 0, we stop the process.

Step 7: The HCF is the divisor of the last non-zero remainder.
In this case, the divisor of the last non-zero remainder (188) is 188.

Therefore, the HCF of 1488 and 37888 is 188.

Explanation:
Euclid’s division algorithm is based on the principle that if we subtract the smaller number from the larger number, the HCF of the two numbers will remain the same. The algorithm involves repeated divisions until a remainder of zero is obtained. The divisor of the last non-zero remainder is the HCF of the two numbers.

In this case, we started by dividing 37888 by 1488. The remainder was 188. Then, we divided 1488 by 188, and the remainder was 0. Since we obtained a remainder of 0, we stopped the process. The divisor of the last non-zero remainder (188) is the HCF of 1488 and 37888.

Using Euclid’s division algorithm allows us to find the HCF efficiently by reducing the numbers involved in each step. It is a simple and effective method for finding the HCF of any two numbers.